Abstract: In this paper we give a categorical treatment of matrix Toda brackets, both in the pre- and post-compositional versions. Explicitly the setting in which we work is, à la Gabriel-Zisman, a -category with zeros. The development parallels that in the topological setting but with homotopy groups replaced by nullity groups of invertible -morphisms. A central notion is that of conjugation of -morphisms. Our treatment of matrix Toda brackets is carried forward to the point of establishing appropriate indeterminacies.